reserve k,n for Element of NAT,
  a,Y for set,
  D,D1,D2 for non empty set,
  p,q for FinSequence of NAT;
reserve F,F1,G,G1,H,H1,H2 for CTL-formula;
reserve sq,sq9 for FinSequence;
reserve V for CTLModel;
reserve Kai for Function of atomic_WFF,the BasicAssign of V;
reserve f,f1,f2 for Function of CTL_WFF,the carrier of V;
reserve S for non empty set;
reserve R for total Relation of S,S;
reserve s,s0,s1 for Element of S;
reserve BASSIGN for non empty Subset of ModelSP(S);
reserve kai for Function of atomic_WFF,the BasicAssign of BASSModel(R,BASSIGN);

theorem
  for f, g being Assign of BASSModel(R,BASSIGN) holds SIGMA(f) = SIGMA(g)
  implies f=g
proof
  let f,g be Assign of BASSModel(R,BASSIGN);
  assume
A1: SIGMA(f) = SIGMA(g);
  SIGMA(f) = { s where s is Element of S : (Fid(f,S)).s=TRUE } by Lm40;
  then { s where s is Element of S : (Fid(f,S)).s=TRUE } = { s where s is
  Element of S : (Fid(g,S)).s=TRUE } by A1,Lm40;
  hence thesis by Lm41,Lm42;
end;
